Two-particle Kapitza-Dirac diffraction

We extend the study of Kapitza-Dirac diffraction to the case of two-particle systems. Due to the exchange effects the shape and visibility of the two-particle detection patterns show important differences for identical and distinguishable particles. We also identify a novel quantum statistics effect present in momentum space for some values of the initial particle momenta, which is associated with different numbers of photon absorptions compatible with the final momenta.Comment: Minor changes with the published versio

An open systems approach to calculating time dependent spectra

A new method to calculate the spectrum using cascaded open systems and master equations is presented. The method uses two state analyzer atoms which are coupled to the system of interest, whose spectrum of radiation is read from the excitation of these analyzer atoms. The ordinary definitions of a spectrum uses two-time averages and Fourier-transforms. The present method uses only one-time averages. The method can be used to calculate time dependent as well as stationary spectra.Comment: 8 pages, revtex, 18 figures, to be published in J.Mod.Op

X-ray Emission from SN 2012ca: A Type Ia-CSM Supernova Explosion in a Dense Surrounding Medium

X-ray emission is one of the signposts of circumstellar interaction in supernovae (SNe), but until now, it has been observed only in core-collapse SNe. The level of thermal X-ray emission is a direct measure of the density of the circumstellar medium (CSM), and the absence of X-ray emission from Type Ia SNe has been interpreted as a sign of a very low density CSM. In this paper, we report late-time (500--800 days after discovery) X-ray detections of SN 2012ca in {\it Chandra} data. The presence of hydrogen in the initial spectrum led to a classification of Type Ia-CSM, ostensibly making it the first SN~Ia detected with X-rays. Our analysis of the X-ray data favors an asymmetric medium, with a high-density component which supplies the X-ray emission. The data suggest a number density $> 10^8$ cm$^{-3}$ in the higher-density medium, which is consistent with the large observed Balmer decrement if it arises from collisional excitation. This is high compared to most core-collapse SNe, but it may be consistent with densities suggested for some Type IIn or superluminous SNe. If SN 2012ca is a thermonuclear SN, the large CSM density could imply clumps in the wind, or a dense torus or disk, consistent with the single-degenerate channel. A remote possibility for a core-degenerate channel involves a white dwarf merging with the degenerate core of an asymptotic giant branch star shortly before the explosion, leading to a common envelope around the SN.Comment: 11 pages, 4 figures. Accepted to MNRA

On IC 10 X-1, the Most Massive Known Stellar-Mass Black Hole

IC 10 X-1 is a variable X-ray source in the Local Group starburst galaxy IC 10 whose optical counterpart is a Wolf-Rayet (WR) star. Prestwich et al. (2007) recently proposed that it contains the most massive known stellar-mass black hole (23-34 M_sun), but their conclusion was based on radial velocities derived from only a few optical spectra, the most important of which was seriously affected by a CCD defect. Here we present new spectra of the WR star, spanning one month, obtained with the Keck-I 10 m telescope. The spectra show a periodic shift in the He II 4686 Ang. emission line as compared with IC 10 nebular lines such as [O III] 5007 Ang. From this, we calculate a period of 34.93+/-0.04 hr (consistent with the X-ray period of 34.40+/-0.83 hr reported by Prestwich et al. 2007) and a radial-velocity semi-amplitude of 370+/-20 km/s. The resulting mass function is 7.64+/-1.26 M_sun, consistent with that of Prestwich et al. (2007) (7.8 M_sun). This, combined with the previously estimated (from spectra) mass of 35 M_sun for the WR star, yields a minimum primary mass of 32.7+/-2.6 M_sun. Even if the WR star has a mass of only 17 M_sun, the minimum primary mass is 23.1+/-2.1 M_sun. Thus, IC 10 X-1 is indeed a WR/black-hole binary containing the most massive known stellar-mass black hole.Comment: 4 pages, 4 figures, submitted to ApJ

Topological phase for entangled two-qubit states and the representation of the SO(3)group

We discuss the representation of the $SO(3)$ group by two-qubit maximally entangled states (MES). We analyze the correspondence between $SO(3)$ and the set of two-qubit MES which are experimentally realizable. As a result, we offer a new interpretation of some recently proposed experiments based on MES. Employing the tools of quantum optics we treat in terms of two-qubit MES some classical experiments in neutron interferometry, which showed the $\pi$-phase accrued by a spin-$1/2$ particle precessing in a magnetic field. By so doing, we can analyze the extent to which the recently proposed experiments - and future ones of the same sort - would involve essentially new physical aspects as compared with those performed in the past. We argue that the proposed experiments do extend the possibilities for displaying the double connectedness of $SO(3)$, although for that to be the case it results necessary to map elements of $SU(2)$ onto physical operations acting on two-level systems.Comment: 25 pages, 9 figure

Selmer Groups in Twist Families of Elliptic Curves

The aim of this article is to give some numerical data related to the order of the Selmer groups in twist families of elliptic curves. To do this we assume the Birch and Swinnerton-Dyer conjecture is true and we use a celebrated theorem of Waldspurger to get a fast algorithm to compute $$. Having an extensive amount of data we compare the distribution of the order of the Selmer groups by functions of type $\alpha \frac{(\log \log (X))^{1+\varepsilon}}{\log (X)}$ with $\varepsilon$ small. We discuss how the "best choice" of $\alpha$ is depending on the conductor of the chosen elliptic curves and the congruence classes of twist factors.Comment: to appear in Quaestiones Mathematicae. 16 page